Optimum efficiency of a three-way catalyst is achieved when a spark ignited internal combustion engine operates at stoichiometry (i.e., ideal air-to-fuel ratio). This requires that the in-cylinder air charge (i.e., mass flow rate of air into the cylinder) be matched by an appropriate amount of fuel. At each engine event, in-cylinder air-charge is typically estimated based on the measurements from a throttle mass air flow (MAF) sensor or an intake manifold pressure (MAP) sensor.
However, the present air-charge estimate, which pertains to the cylinder presently on the intake stroke, is several (typically one or two) engine events late for a fueling decision. This happens because the optimal timing for fuel injection in port fuel injection engines is on the closed intake valve. Moreover, dispensing the fuel takes a finite amount of time and larger quantities at higher engine speed may not be dispensed in one event or less. Thus, the amount of fuel decided at time t will be dispensed into the port of a cylinder that is to start its intake several engine events into the future. An improvement in the ability to control air/fuel ratio will follow if future values of cylinder air-charge can be predicted based on the present and past measurement of engine operating conditions. Because measurement noise has detrimental effect on the accuracy of prediction, the challenge for the designer is to provide a system that responds fast to legitimate changes in the signals being measured, yet is robust against inevitable measurement noise.
Several methods have been established that predict air charge for future cylinder events. For example, U.S. Pat. No. 4,512,318, issued to Ito et al., discloses a method for correcting the fuel injection flow rate in order to obtain an ideal air/fuel ratio. A "correction coefficient" (a multiplier for the base fuel injection time) is determined based on the rates of change of the currently measured intake manifold pressure and throttle valve position signals.
Similarly, a second known method disclosed in U.S. Pat. No. 5,497,329, issued to Tang, addresses a method of predicting air mass induced into each cylinder based on a predicted value of MAP. The predicted value of MAP is based on the rates of change of the intake manifold pressure signal and the sensed throttle position. These methods are signal-based, non-recursive predictors. These methods fail to take into account the available model of the manifold filling dynamics thereby making the predictions sensitive to noise and prone to overshooting.
A prediction method based on the theory of Kalman Filtering has been disclosed in U.S. Pat. Nos. 5,270,935 and 5,273,019, issued to Dudek et al. and Matthews et al., respectively. Kalman filters are designed for linearized models obtained by standard least squares identification. The algorithms disclosed therein are "absolute" predictors wherein the modeling errors affect the predictions in steady state.